This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic conver...

Symmetries play an important role in the dynamics of physical systems. As example, quantum physics and microworld are basis symmetry principles. These problems reduced to solving inequalities general. That is why this article, we study numerical approximation solutions variational inequality involving quasimonotone operators infinite-dimensional real Hilbert space. We prove that iterative seque...

We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansivemappings, the set of solutions of a variational inclusion with set-valued maximal monotone mapping, and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theo...

In this paper, we introduce an iterative method for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusions with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of an equilibrium problem in Hilbert spaces. Furthermore, using our new iterative scheme, unde...

In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method Malitsky Tam for finding a zero sum two monotone operators in real Hilbert space. Our proposed methods only require one forward evaluation single-valued operator backward set-valued at each iteration; feature that is absent many other available literature. We also develop ...

Abstract The primary goal of this research is to investigate the approximate numerical solution variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In study, sequence obtained by proposed iterative technique for solving converges strongly toward a due viscosity-type scheme. Furthermore, new that uses an inertial mechanism obtain strong convergence...

Let C be a closed convex subset of a real Hilbert space H . Let A be an inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C . We introduce two iteration schemes of finding a point of (A+B)−10, where (A+B)−10 is the set of zero points of A+B. Then, we prove two strong convergence theorems of Halpern’s type in a Hi...

In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we ...